{"paper":{"title":"Equivalence between nonlinear dynamical systems and urn processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.DS"],"primary_cat":"nlin.CD","authors_text":"Annibal Figueiredo, Benito Hern\\'andez-Bermejo, Iram Gleria, L\\'eon Brenig, Tarc\\'isio M. Rocha Filho","submitted_at":"2018-07-17T12:53:31Z","abstract_excerpt":"An equivalence is shown between a large class of deterministic dynamical systems and a class of stochastic processes, the balanced urn processes. These dynamical systems are governed by quasi-polynomial differential systems that are widely used in mathematical modeling while urn processes are actively studied in combinatorics and probability theory. The presented equivalence extends a theorem by Flajolet et al. (Flajolet, Dumas and Puyhaubert Discr. Math. Theor. Comp. Sc. AG - 2006, DMTCS Proceedings) already establishing an isomorphism between urn processes and a particular class of different"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.06392","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}